What is the math behind the profile's "Fleet Power"

Tl;DR: The fatal flaw in your attempts to find a formula is that you assume a linear function. The function is most likely based on c * sqrt(X), where X is total stats of your fleet and c is some arbitrary constant chosen by the developer.

Long answer: I started playing less than two weeks ago, so I have a new account where I can do some low-end testing. I am currently much closer to ~1FP for every ~60 total stats; raising a ship's power by ~230 will give me 3-4 Fleet Power. On the other hand, if I look at the leaderboards, the top ranked players have only about 6x as much Fleet Power as me (12000 vs. 2000), but I'd expect their total stats to be at least 20 times as high as mine.

On a side note, moving all the gear from my strongest to my weakest destroyer (after stripping the weaker one down) had no effect on my Fleet Power. Javelin went from 3191 to 2039 Power (-1152), Cygnet went from 672 to 1824 (+1152), and my Fleet power remained at 2066. Dismissing duplicate ships has no effect, and neither does collecting or powering up Collab ships.

The obvious conclusion is that, the higher your total stats already are, the more stats you have to gain to increase your fleet power. This assumption should explain all the observations in your data, e.g. a new ship giving 6-7 Fleet Power early on and only 2 Fleet Power later on.

The developers have a simple reason for doing this: Making the leaderboards look less intimidating for new players and giving them the illusion that they might be able to catch up. On the other hand, there would be no reason for the devs to calculate all the different variables you gathered and plugging them into a formula.